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Question

A block of wood floats in water with (45)th of its volume submerged. If the same block just floats in a liquid, the density of the liquid (in kg m−3) is:

A
1250
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B
600
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C
400
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D
800
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Solution

The correct option is D 800
According to Archimede's principle Weight of the body = Weight of the liquid displaced Let V be volume of block.
In water, Vρblockg=(45V)ρwaterg
ρblock=45ρweter ....(i)
In liquid, Vρblockg=Vρliquidg
ρblock=ρliquid .....(ii)
From (i) and (ii), we get
ρLiquid=45ρwater=45×103kgm3=800kgm3

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